Option 1: Explicitly Define the Domains

if ($_SERVER['HTTP_HOST'] == 'www.mywebsite.com') {
    define('WP_SITEURL', 'http://www.mywebsite.com');
    define('WP_HOME',    'http://www.mywebsite.com');
} else {
    // this is the default that shows up if someone visits your site
    define('WP_SITEURL', 'http://www.mywebsite.net');
    define('WP_HOME',    'http://www.mywebsite.net');
}

Source: Run Multiple Domains with One WordPress Instance – WPLauncher